Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
finite field
|
| gptkbp:additiveGroup |
abelian
|
| gptkbp:allFiniteFieldsAreIsomorphic |
if same order
|
| gptkbp:alsoKnownAs |
gptkb:Galois_field
|
| gptkbp:automorphismGroup |
cyclic group of order n
|
| gptkbp:characteristic |
prime number p
|
| gptkbp:containsSubfield |
𝔽_p
|
| gptkbp:degreeOfExtension |
n
|
| gptkbp:everyElementSatisfies |
x^q = x
|
| gptkbp:extensionFieldOf |
𝔽_p
|
| gptkbp:fieldCharacteristic |
p
|
| gptkbp:FrobeniusAutomorphism |
x ↦ x^p
|
| https://www.w3.org/2000/01/rdf-schema#label |
𝔽 q
|
| gptkbp:irreduciblePolynomialDegree |
n
|
| gptkbp:multiplicativeGroup |
cyclic
|
| gptkbp:notation |
gptkb:GF(q)
F_q |
| gptkbp:numberOfRooms |
q
|
| gptkbp:order |
q
|
| gptkbp:primitiveElementExists |
true
|
| gptkbp:q |
prime power
|
| gptkbp:splittingFieldOf |
x^q - x over 𝔽_p
|
| gptkbp:structure |
vector space over 𝔽_p
|
| gptkbp:uniqueUpToIsomorphism |
true
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
coding theory cryptography number theory combinatorics |
| gptkbp:bfsParent |
gptkb:Galois_fields
|
| gptkbp:bfsLayer |
6
|